Cognitively Guided Instruction is "a

professional development Professional development is learning to earn or maintain professional credentials such as academic degrees to formal coursework, attending conferences, and informal learning opportunities situated in practice. It has been described as intensiv ...

program based on an integrated program of research on (a) the development of students' mathematical thinking; (b) instruction that influences that development; (c) teachers' knowledge and beliefs that influence their instructional practice; and (d) the way that teachers' knowledge, beliefs, and practices are influenced by their understanding of students' mathematical thinking". CGI is an approach to teaching mathematics rather than a curriculum program. At the core of this approach is the practice of listening to children's mathematical thinking and using it as a basis for instruction. Research based frameworks of children's thinking in the domains of addition and subtraction, multiplication and division, base-ten concepts, multidigit operations, algebra, geometry and fractions provide guidance to teachers about listening to their students.

Case studies A case study is an in-depth, detailed examination of a particular case (or cases) within a real-world context. For example, case studies in medicine may focus on an individual patient or ailment; case studies in business might cover a particular ...

of teachers using CGI have shown the most accomplished teachers use a variety of practices to extend children's mathematical thinking. It's a tenet of CGI that there is no one way to implement the approach and that teachers' professional judgment is central to making decisions about how to use information about children's thinking. The research base on children' mathematical thinking upon which CGI is based shows that children are able to solve problems without

direct instruction Direct Instruction (DI) is a term for the explicit teaching of a skill-set using lectures or demonstrations of the material to students. A particular subset of direct instruction, denoted by capitalization as Direct Instruction, refers to a speci ...

by drawing upon informal knowledge of everyday situations. For example, a study of kindergarten childrenCarpenter, et al., 1993 showed that young children can solve problems involving what are normally considered advanced mathematics such as multiplication, division, and multistep problems, by using direct modeling. Direct modeling is an approach to

problem solving Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business an ...

in which the child, in the absence of more sophisticated knowledge of mathematics, constructs a solution to a story problem by modeling the action or structure. For example, about half of the children in a study of kindergartners' problem solving were able to solve this multistep problem, which they had never seen before, using direct modeling: ''19 children are taking a mini-bus to the zoo. They will have to sit either 2 or 3 to a seat. The bus has 7 seats. How many children will have to sit three to a seat, and how many can sit two to a seat?'' :''Example'': Fred had six marbles at school. On the way home from school his friend Joey gave him some more marbles. Now Fred has eleven marbles. How many marbles did Joey give to Fred? Students may solve this problem by counting down from eleven or by counting up from six. With the use of manipulatives students would be able to represent their thoughts for this problem multiple ways. For instance, they might make a row of six counting blocks next to a row of eleven counting blocks and then compare the difference. The CGI philosophy is detailed in
Children's Mathematics
' which is co-authored by Thomas Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi, and Susan Empson.

References

;Notes *Carpenter, T. P., Ansell, E., Franke, M. L., Fennema, E. & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem-solving processes. Journal for Research in

Mathematics Education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although ...

, 24(5), 427–440. *Carpenter, T., Fennema, E., Franke, M., L. Levi, and S. Empson. ''Children's Mathematics, Second Edition: Cognitively Guided Instruction''. Portsmouth, NH: Heinemann, 2014. *Carpenter, T. P., Fennema, E., Franke, M., Levi, L. & Empson, S. B. (2000). Cognitively Guided Instruction: A Research-Based Teacher Professional Development Program for Mathematics.

Research Report A research report is a publication that reports on the findings of a research project or alternatively scientific observations on or about a subject. Research reports are produced by many sectors including industry, education, government and non-g ...

03. Madison, WI: Wisconsin Center for Education Research.
Report on CGI effectivenss
{{Mathematics education Elementary mathematics Mathematics education